Analysis of the Pairing Interaction in the Cuprates

Thermal difference reflectance (TDR) spectra taken on a large number of superconducting cuprates has enabled us to determine the energy dependence and strength of the pairing interaction in each. All show strong contributions from the phonons and a smaller, but significant contribution from an electronic transition near 1.7 eV. Recent improvements in the signal-to-noise ratio have revealed that the electronic excitation is accompanied in all cases by a weaker companion about 0.5 eV lower in energy. No other contributions are found. We identify these transitions as the d_z2 to d_x2–y2 excitations of the Cu ion in the 3d⁹ and 3d⁸ states, respectively, and have calculated the coupling strength mediated by each. The calculated values agree in order of magnitude with the observed strengths. We find that, in addition to the direct electronic coupling that corresponds to an electron–phonon-like term, the overlap between the oxygen and the copper orbitals leads to an exchange term. The direct term couples only to an s-wave gap, as for phonons, while the exchange term couples s-wave to d-wave, and vice versa. We discuss the consequences of this result.